One of the greatest assets of a secretary is often his/her ability on the keyboard of a computer. Mrs. Garcia has been recognized as the Most Outstanding Typist at a prestigious firm because of her outstanding typing speed. The table below displays data collected from her most recent evaluation.
minutes 1 2 3 4
words 70 140 210 280
Write an equation to represent the total number of words, y, that Mrs. Garcia can type in x minutes
If Mrs. Garcia maintains a constant speed consistent with the results above, how many words will she type in 49 minutes
To find the equation to represent the total number of words typed in x minutes by Mrs. Garcia, we will first find the rate at which she types.
The rate of typing can be calculated by finding the slope of the data points. We can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Using the data points (1, 70) and (2, 140), we get:
m = (140 - 70) / (2 - 1) = 70 words per minute
Now that we have the rate of typing, we can write the equation in slope-intercept form:
y = mx + b
y = 70x + b
To find the value of b, we can use any of the data points. Let's use (1, 70):
70 = 70(1) + b
70 = 70 + b
b = 0
Therefore, the equation representing the total number of words, y, that Mrs. Garcia can type in x minutes is:
y = 70x
To find out how many words Mrs. Garcia will type in 49 minutes, we substitute x = 49 into the equation:
y = 70(49) = 3430
Mrs. Garcia will type 3430 words in 49 minutes.